Stochastic Process
The stochastic_process
module consists of classes and functions to generate samples of stochastic processes from
prescribed properties of the process (e.g. power spectrum, bispectrum and/or autocorrelation function). The existing
classes rely on stochastic expansions taking the following general form,
such that the process can be expressed in terms of a set of uncorrelated random variables, \(\theta(\omega)\), and deterministic basis functions \(\phi(x)\).
The stochastic_process
module supports simulation of uni-variate, multi-variate, multi-dimensional, Gaussian
and non-Gaussian stochastic processes. Gaussian stochasitc processes can be simulated using the widely-used Spectral
Representation Method ([43], [44], [45], [46])
and the Karhunen-Loeve Expansion ([47], [48], [49]). Non-Gaussian
stochastic processes can be generated through higher-order spectral representations ([50], [51],
[52]) or through a
nonlinear transformation from a Gaussian stochastic process to a prescribed marginal distribution using translation
process theory [53]. Modeling of arbitrarily distributed random processes with specified correlation and/or power
spectrum can be performed using the Iterative Translation Approximation Method (ITAM) ([54], [55]) for inverse
translation process modeling.
This module contains functionality for all the stochastic process methods supported in UQpy.
The module currently contains the following classes:
SpectralRepresentation
: Class for simulation of Gaussian stochastic processes and random fields using the Spectral Representation Method.BispectralRepresentation
: Class for simulation of third-order non-Gaussian stochastic processes and random fields using the Bispectral Representation Method.KarhunenLoeveExpansion
: Class for simulation of stochastic processes using the Karhunen-Loeve Expansion.Translation
: Class for transforming a Gaussian stochastic process to a non-Gaussian stochastic process with prescribed marginal probability distribution.InverseTranslation
: Call for identifying an underlying Gaussian stochastic process for a non-Gaussian process with prescribed marginal probability distribution and autocorrelation function / power spectrum.
As with other modules of UQpy
, adding simulation methods requires the user to build a new class to support
the desired functionality. It does not require modification of any existing classes or methods.